One of the cardinal virtues is prudence
, which St. Thomas Aquinas ranked first among the cardinal virtues and which Aristotle defined as "right reason applied to practice" (source
). When assessing any given course of action, including evangelism, a Christian is expected to exercise prudence.
Look at the situation that was under consideration: A Catholic wanted to know what to do about friendship with an "unabashedly gay" coworker. This is not someone with whom the inquirer is tied by bonds of hearth or home (neighbor or family). This is not someone with whom any personal relationship must
be fostered. This is a coworker, and all that is required of a relationship with a coworker is professional respect and courtesy.
Prudence also demands looking at the probable results. That is why I noted that, in the current social climate, the Catholic's job could be put in jeopardy if he tells a homosexual coworker what he thinks of the homosexual's chosen lifestyle. If the Catholic has family in need of his support, then his actions could negatively impact them. And to what purpose? Is there any good reason to suppose that an "unabashedly gay" person is going to change his way of life because a Catholic coworker tells him what the Catholic thinks about his lifestyle? Perhaps a more prudent course of action with a coworker is to pray and to offer up personal sacrifices for his conversion (which might entail asking God to bring into his life someone with more freedom to speak more frankly to him about his lifestyle choices).
If this homosexual was not a coworker, but was instead a family member or longstanding social friend, then a different course of action might be appropriate. But, again, that is determined by exercising prudence in assessing all aspects of the situation.